The non-split symplectic period of a residual Eisenstein series on Sp2n

Let F be a number field with ring of adeles A, let K be a quadratic extension of F with ring of adeles A(K). Let eta be an irreducible, automorphic, cuspidal, self-dual representation of GL(2n) (A) and let phi is an element of Ind(P(A))(Sp2n(A)) eta, where P is the standard Siegel parabolic. We present an identity between the Sp(n) (A(K))-period of the residual Eisenstein series on Sp(2n) (A) associated to phi and the GL(n) (A(K))-period of phi. This is a non-split version of a result of Ginzburg, Soudry and Rallis.